Research Article A PLS-Based Weighted Artificial Neural Network Approach for Alpha Radioactivity Prediction inside Contaminated Pipes

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1 Mathematical Problems in Engineering, Article ID , 5 pages Research Article A PLS-Based Weighted Artificial Neural Network Approach for Alpha Radioactivity Prediction inside Contaminated Pipes Xianguo Tuo, 1,2 Mingzhe Liu, 2 Lei Wang, 2 Jianbo Yang, 2 and Yi Cheng 2 1 Key Subject Laboratory of National Defense for Radioactive Waste and Environmental Security, Southwest University of Science and Technology, Mianyang , China 2 State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu , China Correspondence should be addressed to Mingzhe Liu; liumz@cduteducn Received 17 October 2013; Revised 26 February 2014; Accepted 28 February 2014; Published 23 March 2014 Academic Editor: Wei Bian Copyright 2014 Xianguo Tuo et al This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited Long-range alpha detection (LRAD) has been used to measure alpha particles emitting contamination inside decommissioned steel pipes There exists a complex nonlinear relationship between input parameters and measuring results The input parameters, for example, pipe diameter, pipe length, distance to radioactive source, radioactive source strength, wind speed, and flux, exhibit different contributions to the measuring results To reflect these characteristics and estimate alpha radioactivity as exactly as possible, a hybrid partial least square back propagation (PLSBP) neural network approach is presented in this paper In this model, each node in the input layer is weighted, which indicates that different input nodes have different contributions on the system and this finding has been little reported The weights are determined by the PLS After this modification, a variety of normal threelayered BP networks are developed The comparison of computational results of the proposed approach with traditional BP model and experiments confirms its clear advantage for dealing with this complex nonlinear estimation Thus, an integrated picture of alpha particle activity inside contaminated pipes can be obtained 1 Introduction With the rapid development of nuclear industry over the last 50 years, nuclear decommissioning has been paid more attention recently Most nuclear facility dismantling is involved in contaminated pipe disassembling The radioactivity of contaminatedpipeswillbefirstlymeasuredtoensurethe safety of operators and environment A long-range alpha detection (LRAD) technique has been presented to measure alpha particles emitting contamination inside pipes [1 7] The corresponding LRAD instrument has been developed, which consists of five units: (1) detection unit; (2) air drive unit; (3) power supply unit; (4) signal acquisition unit; (5) data processing control and display unit The basic idea of the LRAD can be described as follows When air is exposed to alpha radiation, ions are generated The detector system collects the ions and counts the number of ions produced by the radiation The number of ions is proportional to the amount of emitting alpha Thus, the system can indirectly measure contamination inside pipes Figure 1 shows the LRAD measuring instrument used in the experiments, which is developed by our own research group Normally, the result of a LRAD measurement mainly depends on the following six parameters: pipe diameter, pipe length, distance to radioactive source, radioactive source strength, flux, and wind speed The statistical analysis to LRAD measurement results indicates that there is a complex nonlinear relationship between the parameter space and measuring results In particular, it is found that there is an approximate log relation between the distance to the source and the results, while the pipe length exhibits a double-peak relation to the results That is to say, the multiple parameter effects are quite obvious Thus, How to distinguish different contributions of different input parameters has been a focus in the system To the best of our knowledge, this issue has been little studied using a hybrid artificial neural network (ANN) method so far

2 2 Mathematical Problems in Engineering 2 Hybrid PLSBP Model The alpha radioactivity estimation can be solved by constructing a model which represents the relationship between the measuring variables and the measuring results This constructedmodelcanbeusedtocalculatethemeasuring results from the measured variables of LRAD instrument In general, the model to be built can be written as Figure 1: Illustration of the LRAD experimental installation ANN methods especially back propagation (BP) models have been recognized as more efficient models than the conventional statistical forecasting ones for solving nonlinear issues However, BP models have two main flaws, that is, tendency to overfitting and difficulty to determine the optimal number of the hidden-layer nodes Recently, a lot ofimprovedbpmodelsbasedonpartialleastsquare(pls) have been presented and applied to various fields in solving nonlinear issues from natural to man-made systems [8 15] Medhat presented two methodologies, namely, partial mutual information and self-organizing map, integrated with a genetic algorithm and general regression neural network [12] Jain and Kumar applied a hybrid neural network model for hydrologic time series forecasting [13] Research [8] uses the PLS to choose the BP network architecture and initial weights between nodes In [9], the PLS is added between the hidden layer and the output layer in order to check and remove the correlation among the nonlinear transformed variables in a three-layered BP network In [10], PLS isused to decrease the abundance of input variables; that is, PLS plays a preprocessing role in a three-layered BP network In [11], in order to study gas-solid adsorption process, PLS serves for data compression and noise reduction before a normal threelayered BP network is performed AlthoughhybridANNmodelshavefoundmanyapplications in a variety of areas, those models normally assumed that contribution of all input nodes is nondiscriminable, that is, homogeneous In fact, different input nodes could have different contributions on the system This issue, that is, the weighted input nodes, has been little considered, to the best of our knowledge Based on excellent ANN research works in the literature and our experimental results obtained from the LRAD, this paper presents a hybrid PLS and BP (PLSBP) model for alpha radioactivity assessment The weighted input nodes can be described by the PLS This is a novel of the paper and a difference from other ANN papers The computational resultsoftheplsbpapproachhaveshownitsclearadvantage for dealing with this complex nonlinear problem, compared to traditional ANN models ThispaperisorganizedasfollowsInSection 2,thehybrid PLSBP model is proposed to take different contributions on the input nodes into account Section 3 analyzes the results of LRAD experiments using the PLSBP model and compares them with measured values The conclusion is given in Section 4 y=f(x), (1) where y is the measuring results and x isavectorofmeasured variables of LRAD instrument, particularly, and x is a vector of n mmatrix and y consists of a m 1matrix in this paper 21 PLS Algorithm The normal PLS algorithm can be described as follows (a) Preprocess data Both x and y variables are normalized by decimal scaling Consider x ij = x ij x j s j, y i = y i y s y, (2) where x j is the average of x j and s j is the standard deviation of x j Similarly,y and s y are the average and the standard deviation of y,respectivelythen,seth= 1, E 0 =(x ij ),andf n m 0 =(y i ) m 1 (b) Calculate the weight vectors w h (c) Calculate the score vectors t h w h =E T h 1 F h 1 (3) t h =E h 1 w h (4) (d) Calculate the loading vectors of x and y p h = ET h 1 t h (t T h t h), (e) Calculate the residuals q h = FT h 1 t h (t T h t h) (5) E h =E h 1 t h p T h, F h =F h 1 q h t h (6) (f) Check the cross validation If Q 2 h 00975, component t h is extracted Then, check t h+1 (g) Repeat (b) (f) unless all components t 1,,t m are obtained 22 PLSBP Algorithm The PLSBP algorithm is developed as follows (a) Preprocess latent variables The components t 1,,t m obtained in the last subsection will be normalized The minimum-maximum normalization is highly recommended for neural networks and is adopted here

3 Mathematical Problems in Engineering 3 30 x 1 t 1 25 x 2 t 2 20 x 3 x m PLS t 3 t n PLS coefficients Latent variables Input layer Hidden layer Output layer Figure 2: Schematic diagram of PLSBP network structure t 1 t 2 t 3 t 4 t 5 t 6 Latent variables (b) Transfer X spacetoanewx space via PLS coefficients (x ij ) n m = (x ij) n m x(t i ) m 1, (7) where (x ij ) and (x n m ij) n m are transferred and original input matrixes, respectively (t i ) m 1 is a minimum-maximum normalized latent variable matrix Equation (7) reflects the contribution of input nodes (c) (x ij ) as a new input matrix is fed into the BP n m network The BP network consists of input layer, hidden layer, and output layer The PLS algorithm is usedtogetlatentvariables(t 1,t 2,,t m ) from the source data X space The latent variables may be viewed as a contribution to the input nodes and fed into the BP network Figure 2 illustrates the PLSBP network structure 3 Computational Results As mentioned above, six LRAD parameters for pipe contamination are involved, that is, pipe diameter, pipe length, distance to radioactive source, radioactive strength, wind speed, and flux Thus, the network includes 6 inputs and 1 output In total, 200 sampling data were collected, among which 150 samples were used for model training, 30 samples for model testing, and the rest 20 samples for prediction We firstly use the PLS algorithm to get the following regression equation: y = t t t t t t 6, where t 1, t 2, t 3, t 4, t 5, and t 6 represent pipe diameter (mm), pipe length (cm), distance to radioactive source (cm), radioactive strength (Bq), wind speed (m/s), and flux (m 3 /h), respectively The corresponding regression coefficients are shown in Figure 3 It can be seen that wind speed and flux dominate the measurement system These variables are normalized via the minimum-maximum method And the (8) Figure 3: Illustration of PLS latent variables and values Table 1: A list of required model parameters Name of variables Value Training sample φ Validation sample φ Testing sample φ Number of input nodes 6 Number of hidden nodes 6 Number of output nodes 1 Error ε 11 of sample φ Error ε 12 of sample φ Error ε 13 of sample φ Learning 005 Training epochs 1000 Training goal 10 4 new input matrix will be obtained by (7)andfedintotheBP network As the initial connection weights and threshold are randomly chosen, we have carried out this model 20 times We took its 95% confidence interval as neural network ensemble The parameters are listed in Table 1 The most important factor to measure performance of an algorithm is to check its forecasting ability of testing samples Table 2 listed prediction result comparisons of real data, PLSBP, and normal BP Figure 4 shows comparisons of relative errors obtained from the PLSBP and normal BP In the normal BP algorithm, the minimum and maximum of relative errors are and , respectively The averaging relative error is The most relative error is less than 8% However, in the PLSBP, the minimum and maximum of relative errors are and , respectively The averaging relative error is The most relative error is less than 5% It can be seen that the proposed PLSBP algorithm has better prediction accuracy than that of normal BP algorithm

4 4 Mathematical Problems in Engineering Pipe diameter Pipe length Distance to source Table 2: Prediction result comparisons of the PLS and BP Radioactive strength Wind speed Flux Measuring results PLSBP Normal BP Relative errors Normal BP PLSBP Testing samples Figure 4: Comparison of relative errors between PLSBP and normal BP In this paper, we assumed that radioactive source strength and radioactive source position are known to measure ionizing values in order to check the feasibility of the proposed method In practice, the distance or source strength is normally unknown and should be estimated from the ion current Therefore, how to estimate the distance or source strength from the ion current is our next step work 4 Conclusion This paper introduced a hybrid partial least square back propagation neural network (PLSBP) model to predict alpha radioactivity inside decommissioned pipes during nuclear facility disassembling The proposed model considers the different contributions of each input node, which has been paid little attention in the literature The computational results indicate that the PLSBP model has a better prediction performance for alpha radioactivity estimation Once the six parameters are determined, the PLSBP model will give an approximate output, and thus, an integrated picture of alpha particle activity inside contaminated pipes can be obtained This approach may give insight into data processing when main and weak component analysis is involved Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper Acknowledgments The authors gratefully acknowledge the comments and suggestions of the anonymous reviewers, which helped in improving the clarity and the quality of the paper This work was supported by the National Natural Science Foundation of China ( , , and ), Scientific and Technological Support Program of Sichuan Province (2013FZ0022), and the Creative Team Program of Chengdu University of Technology

5 Mathematical Problems in Engineering 5 References [1] D W MacArthur, K S Allander, J A Bounds, and K B Butterfield, Small long-range alpha detector (LRAD) with computer readout, Tech Rep LA MS, Los Alamos National Laboratory, 1991 [2] DWMacArthur, Long-rangealphadetector(LRAD), Tech Rep LA-UR , 1991 [3] D W MacArthur, K S Allander, J A Bounds, D A Close, and J L McAtee, Long-range alpha detector, Health Physics, vol 63,no3,pp ,1992 [4] DWMacArthur,KSAllander,andJLMcAtee, Longrange alpha detector for contamination monitoring, Tech Rep LA- UR , Los Alamos National Laboratory, 1991 [5] R D Bolton, Radon monitoring using long-range alpha detector-based technology, Tech Rep LA-UR , Los Alamos National Laboratory, 1994 [6] D W MacArthur, K S Allander, J A Bounds, and J L McAtee, Lrad-based alpha-particle contamination monitoring of personnel and equipment, Nuclear Technology, vol 102, no 2, pp , 1993 [7]MWRawool-Sullivan,KSAllander,JABoundsetal, Field study of alpha characterization of a D&D site using longrange alpha detectors, Tech Rep LA-UR , Los Alamos National Laboratory, 1994 [8] JLu,SChen,WWang,andHvanZuylen, Ahybridmodel of partial least squares and neural network for traffic incident detection, Expert Systems with Applications, vol 39, no 5, pp , 2012 [9] Y Xuefeng, Hybrid artificial neural network based on BP- PLSR and its application in development of soft sensors, Chemometrics and Intelligent Laboratory Systems, vol103,no 2, pp , 2010 [10] S Li, L Li, R Milliken, and K Song, Hybridization of partial least squares and neural network models for quantifying lunar surface minerals, Icarus, vol 221, pp , 2012 [11] C-B Cai, H-W Yang, B Wang, Y-Y Tao, M-Q Wen, and L Xu, Using near-infrared process analysis to study gas-solid adsorption process as well as its data treatment based on artificial neural network and partial least squares, Vibrational Spectroscopy, vol 56, no 2, pp , 2011 [12] M E Medhat, Artificial intelligence methods applied for quantitative analysis of natural radioactive sources, Annals of Nuclear Energy, vol 45, pp 73 79, 2012 [13] A Jain and A M Kumar, Hybrid neural network models for hydrologic time series forecasting, Applied Soft Computing Journal,vol7,no2,pp ,2007 [14] I Helland, PLS regression and statistical models, Statistics,vol179,pp97 114,1990 [15] Y Zhou, J Wu, and F Qin, Nueral network with partial least square prediction model based on SSA and MGF, in Proceedings of the 6th World Congress on Intelligent Control and Automation, pp , 2006

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